Question

Betty and June are having a discussion about an inequality, 2x - 5 < 33, with a replacement set of {12, 18, 19, 26, 28}. Betty says the solution set is {12, 18, 19} and June says the replacement set is {19, 26, 28}. Is either person correct?

Answer 1

Answer:

NONE of the person is correct.

Step-by-step explanation:

Here, the given expression is:  2 x - 5 < 33

1)  Solution set of Betty is {12, 18, 19}

Checking each value of the set in the equation, we get:

At x  = 12:

2 x - 5 < 33 ⇒ 2 (12)  - 5 < 33

⇒ 24 - 5 < 33 , or 19 < 33, TRUE

At x  = 18:

2 x - 5 < 33 ⇒ 2 (18)  - 5 < 33

⇒ 36 - 5 < 33 , or 31 < 33, TRUE

At x  = 19:

2 x - 5 < 33 ⇒ 2 (19)  - 5 < 33

⇒ 38 - 5 < 33 , or 33 < 33,

FALSE as 33 is NOT less than 33 but equal to 33.

Hence, Solution set of Betty is NOT CORRECT

2)  Solution set of June is {19, 26, 28}

Checking each value of the set in the equation, we get:

At x  = 19:

2 x - 5 < 33 ⇒ 2 (19)  - 5 < 33

⇒ 38 - 5 < 33 , or 33 < 33,

FALSE as 33 is NOT less than 33 but equal to 33.

At x  = 26:

2 x - 5 < 33 ⇒ 2 (26)  - 5 < 33

⇒ 52 - 5 < 33 , or 47 < 33, FALSE

At x  = 28:

2 x - 5 < 33 ⇒ 2 (28)  - 5 < 33

⇒ 56 - 5 < 33 , or 51 < 33,  FALSE

Hence, Solution set of June is NOT CORRECT

Hence,  NONE of the person is correct.